关于同伦满态与覆叠空间

On Homotopy Epimorphisms and Covering Spaces

本文在点标道路连通ＣＷ空间的同伦范畴中，利用同伦推出示性了同伦满态，得出了若ｆ：Ｘ－Ｙ是同伦满态，则对π１Ｙ的任一正规子群Ｈ，升腾映射ｆ：Ｘ（ｆ－１＃（Ｈ））→■（Ｈ）也是同伦满态．

In this paper, we study in the homotopy category of pointed path-connected CW-spaces. Using homotopy pushouts to characterize homotopy epimorphisms, we have the result as follows: If f: X→ Y is a homotopy epimorphism, H is a normal subgroup of π1Y, then the lifting f: X(f#-l(H)) → Y(H) is also a homotopy epimorphism.